Binomial Theorem questions
776 published questions with worked solutions.
- The interval in which x must lie so that the greatest term in the expansion of (1+x)^ 2n has the greatest coefficient, is
- If the coefficients of three consecutive terms in the expansion of (1+x)^n are in the ratio 1:7:42, then the value of n is
- If the (r+1)^ th term in the expansion of ( a^ 1/3 b^ 1/6 + b^ 1/2 a^ 1/6 )^ 21 has equal exponents of both a and b, then value...
- If in the expansion of ( 1x+x x )^5 the ratio of 4^ th term to the 2^ nd is 2 27 ^4, then the value of x can be
- If (1+x)^n=C_0+C_1x+C_2x^2+ +C_nx^n, then the value of _ 0 r<s n (r+s)(C_r+C_s) is
- If a and d are two complex numbers, then the sum to (n+1) terms of the following series aC_0-(a+d)C_1+(a+2d)C_2- is
- If (1+x)^n=C_0+C_1x+C_2x^2+ +C_nx^n, then _ 0 r<s n (r+s)C_rC_s is equal to
- In the expansion of the following expression 1+(1+x)+(1+x)^2+ +(1+x)^n, the coefficient of x^k (0 k n) is
- Statement 1: If _ r=1 ^nr^3 ( ^nC_r ^nC_ r-1 )=196, then the sum of the coefficients of powers of x in the expansion of the...
- ^nC_0- 12 , ^nC_1+ 13 , ^nC_2- +(-1)^n ^nC_n n+1 is equal to
- If the coefficients of the (2r+4)^ th , (r-2)^ th terms in the expansion of (1+x)^ 18 are equal, then the value of r is
- The value of _ n _ r=1 ^n ( _ t=0 ^ r-1 1 5^n ^nC_r ^rC_t 3^t ) is equal to
- The largest value of x for which the fourth term in the expansion (5^ 25 _5 4^x+44 + 1 5^ _5 [3] 2^ x-1 +7 )^8 is 336 is
- If the three consecutive coefficient in the expansion of (1+x)^n are 28, 56 and 70, then the value of n is
- Least positive integer just greater than (1+0.00002)^ 50000 is
- Let a=3^ 1 223 +1 and for all n 3, let f(n)= ^nC_0 a^ n-1 - ^nC_1 a^ n-2 + ^nC_2 a^ n-3 - +(-1)^ n-1 ^nC_ n-1 a^0. If the value...
- The largest real value of x such that _ k=0 ^4 ( 3^ 4-k (4-k)! ) ( x^k k! )= 32 3 is
- Let 1+ _ r=1 ^ 10 (3^r ^ 10 C_r+r ^ 10 C_r )=2^ 10 ( 4^5+ ) where , N and f(x)=x^2-2x-k^2+1. If , lies between the roots of...
- If the middle term in the expansion of ( x2+2 )^8 is 1120; then the sum of possible real values of x is
- If the constant term in the binomial expansion of (x^2- 1x )^n, n N is 15, then the value of n is equal to
Other chapters
Alcohols, Phenols and EthersAldehydes, Ketones and Carboxylic AcidsAlternating CurrentAminesAnatomy of Flowering PlantsAncient Indian HistoryAnimal KingdomApplication of DerivativesArea Under CurveAromatic Compounds and Aryl HalidesAtomsBasic Mathematics and LogarithmBiodiversity and ConservationBiological ClassificationBiomoleculesBiotechnology and Its ApplicationsBiotechnology: Principles and ProcessesBody Fluids and CirculationBreathing and Exchange of GasesCell Cycle and Cell DivisionCell: The Unit of LifeChemical Bonding and Molecular StructureChemical Coordination and IntegrationChemical Kinetics